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access icon free Optimal consensus control of linear multi-agent systems with communication time delay

  • Author(s): Jie Sheng 1  and  Zhengtao Ding 2
    • View affiliations
    • Affiliations: 1: Department of Automation, University of Science and Technology of China, Hefei 230027, People's Republic of China;
      2: Control Systems Centre, School of Electrical and Electronic Engineering, The University of Manchester, Sackville Street Building, Manchester M13 9PL, UK
  • Source: Volume 7, Issue 15, 17 October 2013, p. 1899 – 1905
    DOI:  10.1049/iet-cta.2013.0478 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received 24/05/2013, Accepted 14/08/2013, Revised 13/08/2013, Published

This study investigates the consensus control of linear multi-agent systems with communication time delay. Upon exploring certain features of Laplacian matrix, optimal consensus control conditions are identified using semi-discretisation method that develops a mapping of the system response in a finite-dimensional state space. Consensus region and consensus boundary can be obtained by comparing the maximum absolute value of the mapping's eigenvalues with 1. Besides, minimisation of the maximum absolute value of the eigenvalues leads to optimal control gains representing fastest convergence speed. The proposed control only uses relative state information of the system. Numerical simulations validate the proposed control design and show the performance with different control gains and time delays.

Inspec keywords: linear systems; mobile robots; eigenvalues and eigenfunctions; multi-robot systems; delay systems; matrix algebra; control system synthesis; multidimensional systems; convergence; optimal control

Other keywords: maximum absolute value; communication time delay; optimal control gains; system response mapping; control design; Laplacian matrix; eigenvalues mapping; minimisation; numerical simulations; linear multiagent systems; semidiscretisation method; consensus boundary; consensus region; convergence speed; optimal consensus control conditions; finite-dimensional state space

Subjects: Control system analysis and synthesis methods; Linear algebra (numerical analysis); Optimal control; Distributed parameter control systems; Mobile robots

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